Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation

We study a class of solutions to the SL(2, ℝ)k Knizhnik-Zamolodchikov equation. First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional anti-de Sitter space are discussed. These solutions satisfy the factorization ansa...

Descripción completa

Detalles Bibliográficos
Publicado: 2005
Materias:
AdS/CFT
Conformal field theory
String theory
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0217751X_v20_n20-21_p4821_Giribet
http://hdl.handle.net/20.500.12110/paper_0217751X_v20_n20-21_p4821_Giribet
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0217751X_v20_n20-21_p4821_Giribet
record_format dspace
spelling paper:paper_0217751X_v20_n20-21_p4821_Giribet2023-06-08T15:21:08Z Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation AdS/CFT Conformal field theory String theory We study a class of solutions to the SL(2, ℝ)k Knizhnik-Zamolodchikov equation. First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional anti-de Sitter space are discussed. These solutions satisfy the factorization ansatz and include logarithmic dependence on the SL(2, ℝ)-isospin variables. Different types of logarithmic singularities arising are classified and the interpretation of these is discussed. The logarithms found here fit into the usual pattern of the structure of four-point function of other examples of AdS/CFT correspondence. Composite states arising in the intermediate channels can be identified as the phenomena responsible for the appearance of such singularities in the four-point correlation functions. In addition, logarithmic solutions which are related to nonperturbative (finite k) effects are found. By means of the relation existing between four-point functions in Wess-Zumino-Novikov-Witten model formulated on SL(2, ℝ) and certain five-point functions in Liouville quantum conformal field theory, we show how the reflection symmetry of Liouville theory induces particular ℤ2 symmetry transformations on the WZNW correlators. This observation allows to find relations between different logarithmic solutions. This Liouville description also provides a natural explanation for the appearance of the logarithmic singularities in terms of the operator product expansion between degenerate and puncture fields. © World Scientific Publishing Company. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0217751X_v20_n20-21_p4821_Giribet http://hdl.handle.net/20.500.12110/paper_0217751X_v20_n20-21_p4821_Giribet
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic AdS/CFT
Conformal field theory
String theory
spellingShingle AdS/CFT
Conformal field theory
String theory
Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
topic_facet AdS/CFT
Conformal field theory
String theory
description We study a class of solutions to the SL(2, ℝ)k Knizhnik-Zamolodchikov equation. First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional anti-de Sitter space are discussed. These solutions satisfy the factorization ansatz and include logarithmic dependence on the SL(2, ℝ)-isospin variables. Different types of logarithmic singularities arising are classified and the interpretation of these is discussed. The logarithms found here fit into the usual pattern of the structure of four-point function of other examples of AdS/CFT correspondence. Composite states arising in the intermediate channels can be identified as the phenomena responsible for the appearance of such singularities in the four-point correlation functions. In addition, logarithmic solutions which are related to nonperturbative (finite k) effects are found. By means of the relation existing between four-point functions in Wess-Zumino-Novikov-Witten model formulated on SL(2, ℝ) and certain five-point functions in Liouville quantum conformal field theory, we show how the reflection symmetry of Liouville theory induces particular ℤ2 symmetry transformations on the WZNW correlators. This observation allows to find relations between different logarithmic solutions. This Liouville description also provides a natural explanation for the appearance of the logarithmic singularities in terms of the operator product expansion between degenerate and puncture fields. © World Scientific Publishing Company.
title Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_short Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_full Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_fullStr Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_full_unstemmed Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_sort liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
publishDate 2005
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0217751X_v20_n20-21_p4821_Giribet
http://hdl.handle.net/20.500.12110/paper_0217751X_v20_n20-21_p4821_Giribet
_version_ 1768544270114881536

Ejemplares similares